Finally arriving in Stone, a Midlands town (5)
I believe the answer is:
rugby
'a midlands town' is the definition.
(town in Warwickshire)
'finally arriving in stone' is the wordplay.
'finally' says to take the final letters.
'in' is an insertion indicator.
'stone' becomes 'ruby' (I've seen this before**).
The last letter of 'arriving' is 'g'.
'g' inserted into 'ruby' is 'RUGBY'.
(Other definitions for rugby that I've seen before include "English city; game" , "Sport with oval ball" , "Game with oval ball" , "Town in Warwickshire" , "Famous public school" .)