Girlfriend initially terribly fit for the present (4)
I believe the answer is:
gift
'the present' is the definition.
(I've seen this before)
'girlfriend initially terribly fit' is the wordplay.
'initially' indicates taking the first letters.
'terribly' is an anagram indicator.
The initial letter of 'girlfriend' is 'g'.
'fit' with letters rearranged gives 'ift'.
'g'+'ift'='GIFT'
'for' is the link.
(Other definitions for gift that I've seen before include "Give away" , "Donation" , "Present or special talent" , "Present - natural aptitude" , "''Never look a .... horse in the mouth" .)