Walk around Lake District? (5)
I believe the answer is:
place
'district?' is the definition.
(thesaurus)
'walk around lake' is the wordplay.
'walk' becomes 'pace' (pacing is a kind of walking).
'around' is an insertion indicator.
'lake' becomes 'l'.
'pace' enclosing 'l' is 'PLACE'.
(Other definitions for place that I've seen before include "Spot" , "vacancy" , "square?" , "Locus" , "Scene; put" .)