This topic has been covered a number of times in the past. The short answer is that a large proportion of the senior Saxon nobility, including two of Harold's brothers, was killed at Hastings; a significant number of others fled (including Harold's sons, to Ireland; at least a few went to Byzantium and entered imperial service there); the Normans removed a large number of the remaining Saxon landowners where it seemed safe to do so (meaning predominantly in the south), such that Domesday Book (1086) shows that there were only two remaining large landholders with Saxon names; but that the difficulties of consolidating Norman rule, in what was rather a large kingdom, were great enough for William to leave the northern lords, Edwin of Mercia and Morcar of Northumbria, in place in the immediate post-conquest period even though they had clearly backed Harold in 1066.

When Edwin and Morcar subsequently rebelled in 1068 they were pardoned, but when they did so again in 1069, Edwin's earldom was abolished and the land distributed among several Norman nobles. Morcar, on the other hand, was ultimately replaced by another Northumbrian, Waltheof. Waltheof had spent some time at William's court and would have been well known to the new king, but this decision likely indicates that William still had little confidence in his ability to hold the far north without either Saxon help, or by seriously weakening the forces available to him in the south.

It was only after Waltheof in turn rebelled in 1075 that William installed a Norman Earl of Northumbria, and then only after his infamous Harrying of the North had substantially disrupted and depopulated large swathes of the whole region. His reasons for leaving the large Northumbrian earldom intact, when he had dismembered Mercia, likely had to do with Northumbria's important role as a first line of defence against Scottish incursion, especially in a period where the Scots had the potential to seriously disrupt Norman rule by backing Saxon pretenders.

For a more detailed discussion see

What happened to Anglo-Saxon huscarls, land-owners and mercenaries after the Norman conquest?

and

How devastating really was William the Conqueror's Harrying of the North in 1069-70? I've heard it described as anywhere from a wholesale genocide and slaughter to something more mild. What are the sources and evidence?, both with u/Steelcan909

Was there an organized exodus of Anglo-Saxons after the Norman Invasion? with u/AlanWithTea

How did a tiny, brand-new nobility manage to subjugate [England] in the first place? with u/Viae