Congress heading off cheers about Republican addition? (5)
I believe the answer is:
extra
'addition?' is the definition.
(I've seen this before)
'congress heading off cheers about republican' is the wordplay.
'congress' becomes 'sex' (I've seen this in another clue).
'heading off' means to remove the first letter.
'cheers' becomes 'ta' (both can informally mean thank you).
'about' indicates putting letters inside.
'republican' becomes 'R' (political abbreviation).
'sex' with its first letter removed is 'ex'.
'ta' going around 'r' is 'tra'.
'ex'+'tra'='EXTRA'
(Other definitions for extra that I've seen before include "entry on scorecard?" , "redundant > spear-carrier" , "spotted at rear of the platoon?" , "non-standard item" , "Bit-part actor" .)