What happened to the British officers without men? What happened to the Indian soldiers without officers? What happened to the veterans? How was the British Indian Army split between India and Pakistan? Sorry if this is a lot of questions at once.
"A Matter of Honour" by Philip Mason is probably the single most useful book on the Indian Army. Essentially, the Indian Army had begun a process of "Indianisation" before WW1, with the intention of gradually replacing British Officers with all Indian officers. It was a very gradual process. By WW2 it was in full swing with many more Indians as Ofiicers than before, with many units being entirely officered by Indians. When the Indian Army was expanded in WW2 very large numbers of Indians were trained as Officers. Once WW2 was over and partition and Independence took place, the Indian Army was already going through a process of de-mobilisation and there were, therefore, sufficient Indian and now Pakistani Officers available to take over all commissioned roles in the next couple of years. The British Officers eased them in before either de-mobilising themselves, or transferring to the British Army. Those regiments recruited in the terriory that became Pakistan went to the Pakistani Army, those recruited in Indian territory became Indian Army. Those of the Ghurka regiments that didn't remain British became Indian.