Father and mother going round an American republic (6)
I believe the answer is:
panama
'republic' is the definition.
(I know that Panama is a republic)
'father and mother going round an american' is the wordplay.
'father' becomes 'pa' (pa can mean dad or father).
'and' becomes 'n' (common abbreviation for 'and').
'mother' becomes 'ma' (ma can mean mother).
'going round' is a reversal indicator.
'an american' becomes 'a' (common abbreviation - e.g. in organisation names).
'ma' reversed gives 'am'.
'pa'+'n'+'am'+'a'='PANAMA'
(Other definitions for panama that I've seen before include "isthmus" , "Country and straw hat" , "Hat; Central Am. canal" , "Wide-brimmed hat" , "country divided by boaters?" .)