I have to pursue service that's big (7)
I believe the answer is:
massive
'big' is the definition.
('massive' can be similar in meaning to 'big')
'i have to pursue service' is the wordplay.
'i have' becomes 'ive'.
'to pursue' means one lot of letters go next to another.
'service' becomes 'mass' (I've seen this in other clues).
'ive' put after 'mass' is 'MASSIVE'.
'that's' acts as a link.
(Other definitions for massive that I've seen before include "Large, solid" , "Colossal" , "Great" , "Imposing in size" , "Bulky, weighty" .)