Indian location showing ambition, no end (3)
I believe the answer is:
goa
'indian location' is the definition.
(Goa is a state of India)
'ambition no end' is the wordplay.
'ambition' becomes 'goal' (I've seen this in another clue).
'no end' means to remove the last letter.
'goal' with its final letter removed is 'GOA'.
'showing' acts as a link.
(Other definitions for goa that I've seen before include "Former Portuguese colony on India's west coast" , "Part of West India" , "Suitable place in India" , "Indian region" , "stately annexation of India" .)