Bob's World just stated:
One more mess Great Britain cobbled together as they executed their passage of lines at the end of WWII and said "Here you go Yanks, good luck!"
Yes the British exited South Asia in 1947, ending that imperial era, although we stayed in a few other places till later (more in a moment). At no stage did we conduct a handover to the USA and wish you luck IMHO.

The UK did stay around South Asia, notably through the Cold War, remember CENTO? Effectively the UK relied on diplomacy, although we offered a nuclear umbrella to India after the Indo-China conflict (1961 IIRC) and after 1967 our East of Suez role dwindled. The USA for mainly Cold War reasons got involved in Pakistan, with a dribble of aid into Afghanistan.

IMHO the USA between 1947-1980 paid very little attention to South Asia, you had your own distractions elsewhere in South-East Asia and only returned when the USSR intervened in Afghanistan.