Record of peer touring round this country? (7)
I believe the answer is:
logbook
'record' is the definition.
(I know that logbook is a type of record)
'of peer touring round this country?' is the wordplay.
'of' becomes 'o''.
'peer' becomes 'look' (I've seen this before).
'touring' indicates putting letters inside (touring can mean going round).
'round' indicates putting letters inside.
'this country?' becomes 'GB' (Great Britain).
'o' going within 'look' is 'loook'.
'loook' enclosing 'gb' is 'LOGBOOK'.
(Other definitions for logbook that I've seen before include "Where details of voyages are written" , "official record" , "Ship's record" , "Former vehicle document" , "Car owner's document" .)