They were in pretty much constant contact! By this point in the Middle Ages the Papacy was always in close contact with everyone in the Latin Catholic world. The papal court had a highly sophisticated diplomatic corps, if we can call it that - a chancery that issued and received thousands upon thousands of documents, and various levels of ambassadors who travelled, in person, throughout the Catholic world and even beyond. The crusaders states were no exception to this.

For the First Crusade, the papacy was represented in person by Adhemar, Bishop of Le Puy in France, who was a friend and supporter of Pope Urban II. Along the way the crusaders sent letters back home, including letters to the pope. They also hadn’t really decided what to do if they took Jerusalem, so once they actually did it, what should they do with it? Some people thought they should invite Urban II himself to come and rule it (he had actually died a couple of weeks earlier, without ever knowing they were successful).

In the early years of the kingdom, there was a bit of confusion about who was really in charge. Could they establish a secular monarchy? In hindsight that’s what we say happened, because they ended up with a European-style kingdom with separate political and religious arms, but it wasn’t very clear in 1099 or for a few years afterwards. The first “king”, Godfrey of Bouillon, doesn’t seem to have used the title of king, possibly because he deferred to the authority of the church. His brother Baldwin definitely did take the title of king though.

The crusaders elected a priest named Arnulf of Chocques as their first Latin Patriarch, but the new Pope, Paschal II, didn’t approve - he sent his own representative, Dagobert of Pisa, to act as Patriarch instead. Unlike Adhemar on the First Crusade, Dagobert had more official diplomatic powers - he was a papal legate. A legate was responsible for reporting back to the pope on the circumstances of the crusader states (or wherever else a legate might be sent) and implementing papal policy there.

There were often papal legates in the crusader states for various reasons, and eventually in the 13th century, the office of legate was united with the office of Latin Patriarch, so there was always a legate there as long as there was also a Patriarch. There was also a second Latin Patriarch in Antioch, who was also often (but not necessarily always) a papal legate. One of the thirteenth century legates/patriarchs, Jacques Pantaleon, ended up being elected as Pope Urban IV.

Papal reform movements spread to the crusader states too - issues like education of priests, clerical marriage, irregular elections...the popes had their hands in every issue that involved the church, even in the east. Sometimes the crusaders did their best to ignore instructions from the popes. Over several decades in the 13th century, the crusaders caught the pope’s attention because they were refusing to allow their Muslim slaves to convert to Christianity and be freed from slavery. The pope reminded them that they had to free them, according to church law. The crusaders kept ignoring the pope though, until the pope eventually agreed to let the crusaders keep their slaves, even if the slaves converted. So, sometimes it was difficult to enforce a policy when they were so far away.

Representatives from the crusader states participated in church councils back in Europe. They participated in the ecumenical councils of the Lateran in 1122, 1139, 1179, and 1215. William of Tyre, for example, the famous historian of the crusader states, was present at the Third Lateran Council in 1179, and even wrote a summary of it (though his summary doesn’t survive).

The most practical way to communicate was by sea, and the trip across the Mediterranean took several weeks in good weather. During the spring/summer sailing season, letters and instructions were sent back and forth constantly, and people could travel back and forth too. Cross the Mediterranean in the winter was more dangerous, so for a few months communication might stop. In fact this question reminded me of a project I’m working on, where the timing of some papal letters is important - when Innocent IV became pope in 1243, he immediately wrote a bunch of letters to the crusader states, confirming decisions made by his predecessor (Gregory IX), reaffirming appointments and policies, etc. (My notes say he wrote “a flurry of letters”, haha.) Then there was no communication over the winter, and another “flurry” in the spring of 1244.

The popes could also communicate with the east through monastic and military orders, which were usually dependent directly on the pope rather than any local church. The Knights Templar and Hospitaller, for example, were under the authority of the pope, not the King of Jerusalem or the Latin Patriarch. Since they both had networks of monasteries throughout Europe, it was often easier and faster to communicate through them. They could get information to each other faster than whatever other random merchant ship that might be sailing back and forth. Monastic orders like the benedictines, Cistercians, or Augustinians were also present in the crusader states and they were in contact with the pope or their mother houses back in Europe.

Later in the 12th century, new orders like the Franciscans and Dominicans were established there too. The Dominicans were especially active in the east because their purpose was to preach to non-Catholics. Dominican missionaries were sent out to the crusader states and even further east, all the way to the Mongols and China.

So, in short, the crusader states were always in close contact with the popes. Communication could take a few weeks at least, and over the winter it might slow down a bit or stop entirely, but otherwise both sides were always well aware of each other.

Sources:

Bernard Hamilton, The Latin Church in the Crusader States: The Secular Church (London, 1980)

Malcolm Barber, The Crusader States (Yale University Press, 2012)