West coast county supporting government almost every time (6)
I believe the answer is:
galway
'west coast county' is the definition.
(county on the west coast of Ireland)
'supporting government almost every time' is the wordplay.
'supporting' means one lot of letters go next to another (in a down clue, some letters go under others).
'government' becomes 'g'.
'almost' means to remove the last letter (most of the word but not all of it).
'every time' becomes 'always' (I've seen this before).
'always' with its last letter taken off is 'alway'.
'g' put next to 'alway' is 'GALWAY'.
(Other definitions for galway that I've seen before include "Connacht city" , "Irish city" , "County of W. Ireland" , "flautist" , "Western City of the Tribes" .)