As a rule, grin wryly about a close finish (5)
I believe the answer is:
reign
'as a rule' is the definition.
(I've seen this before)
'grin wryly about a close finish' is the wordplay.
'wryly' indicates anagramming the letters.
'about' is an insertion indicator.
'finish' indicates one should take the final letters.
The last letter of 'close' is 'e'.
'grin' with letters rearranged gives 'rign'.
'rign' going around 'e' is 'REIGN'.
(Other definitions for reign that I've seen before include "Rule as king or queen" , "Period of the rule of a sovereign" , "Sovereignty" , "time in power" , "Monarch's rule" .)