Resort after a time has spread to west and east (7)
I believe the answer is:
margate
'resort' is the definition.
(I have seen 'coastal resort' mean 'margate' so perhaps 'resort' could also mean 'margate')
'a time has spread to west and east' is the wordplay.
'a time' becomes 't' (abbreviation).
'has' means one lot of letters go next to another.
'spread' becomes 'marg' (short for margarine).
'to west' suggests taking the first letters (I've seen 'west of' mean this (most west - leftmost - letter)).
'east' becomes 'e' (abbreviation).
The first letter of 'and' is 'a'.
'marg'+'a'='marga'
't' after 'marga' is 'margat'.
'margat'+'e'='MARGATE'
'after' acts as a link.
(Other definitions for margate that I've seen before include "Kentish Town?" , "which people may visit for seaside holiday" , "resort town" , "coastal resort" , "place in England" .)