Postal service in trouble after excellent run — the end of them (7)
I believe the answer is:
airmail
'postal service' is the definition.
(airmail is a kind of postal service)
'trouble after excellent run the end of them' is the wordplay.
'trouble' becomes 'ail' (synonyms).
'after' means one lot of letters go next to another.
'excellent' becomes 'ai'.
'run' becomes 'r' (cricket abbreviation).
'the end of' suggests the final letters.
The final letter of 'them' is 'm'.
'ai'+'r'+'m'='airm'
'ail' after 'airm' is 'AIRMAIL'.
'in' acts as a link.
(Other definitions for airmail that I've seen before include "overseas post?" , "post far away" , "Way of communicating" , "Letter delivery system" , "Letters sent up" .)