Whose last ball in Test cricket was no-balled, yet he played another 32 Tests for his country?
a batsman…ofcourse. 
Hmm. Either David Gower (English batsmen) or Sayid Kirmani (Pakistan 'keeper). Welcome to the both of you. I’m taking it that you don’t know the answer Gephydrophobia because quiz-type challenges, whilst welcome, belong in the MPSIMS forum. This cricinfo page should be useful, although no dates for the no-ballings are mentioned.
I thought Gower, who I think is recorded in Wisden as no-balled while imitating P.Edmonds, but he bowled 6 overs in test cricket so his last ball cannot have been a no ball. He did hit his first ball in test cricket for 4 however.
Kirmani is an Indian not a Pakistani, but did bowl 3.1 overs in tests, so maybe.
No Kirmani’s second ball in test cricket was a no ball.
I wasn’t sure whether don’t ask had claimed to have the answer (sounded confused but he had it). So, being thorough and playing with Cricinfo’s search engine: from the list I linked to when I WAGged I can rule out:
E Jones (no-balled for throwing in) 1898 (only 19 tests)
GAR Lock 1954 (turned to spin after being no-balled)
GM Griffin 1960 (2 tests)
Haseeb Ahsan 1960 (only 12 tests)
I Meckiff 1963 (18 tests, retired upon being no-balled)
Abid Ali 1968 (turns out to Syed Abid Ali, not the 3 other Abid Alis. Only 29 tests)
HK Olonga 1995 (still playing with changed action)
M Muralitharan 1995 (still playing and bowling. Wrongly accused, too)
GW Flower 2000 (still playing)
DI Gower 1986 (6 completed overs as per don’t ask’s answer)
leaving
SMH Kirmani 1983 Played 88 tests until 1988, so number of tests plausible. 3.1 overs. Bingo.
And the Pakistani 'keeper I was thinking of was Wasim Bari. And no, I’m not going to see whether he ever had a bowl.