At first, Rotherham United got better (7)
I believe the answer is:
rallied
'got better' is the definition.
(I've seen this before)
'at first rotherham united' is the wordplay.
'at' means one lot of letters go next to another.
'first rotherham' becomes 'r' (1st letter of 'rotherham').
'united' becomes 'allied' (similar in meaning).
'r' next to 'allied' is 'RALLIED'.
(Other definitions for rallied that I've seen before include "Recovered strength after illness, or entered driving competition" , "Made a recovery" , "Gathered" , "(Of shares) increased in value after a fall" , "Brought together" .)