Swear the civic centre's at the town centre! (3)
I believe the answer is:
vow
'swear' is the definition.
(I've seen this before)
'civic centre's at the town centre' is the wordplay.
'centre's' indicates the central letters (I've seen 'centred' mean this).
'at' means one lot of letters go next to another.
'the town centre' becomes 'ow' (central letters of the word 'town').
The middle letter of 'civic' is 'v'.
'v'+'ow'='VOW'
'the' is the link.
(Other definitions for vow that I've seen before include "Solemn pledge" , "Oath or solemn promise" , "Binding promise" , "Promise, swear" , "Plight" .)