Girl from Ayr initially going to great trouble (7)
I believe the answer is:
abigail
'girl' is the definition.
'ayr initially going to great trouble' is the wordplay.
'initially' says to take the initial letters.
'going to' is a charade indicator (letters next to each other).
'great' becomes 'big' ('big' can be a synonym of 'great'**).
'trouble' becomes 'ail' ('ail' can be a synonym of 'trouble').
The initial letter of 'ayr' is 'a'.
'a'+'big'+'ail'='ABIGAIL'
'from' is the link.
(Other definitions for abigail that I've seen before include "Girl's name" , "Serving girl" , "Missing party girl" , "Woman's name - old lady's maid" , "Lady's maid (once); David's wife (I. Sam.)" .)