Scotsman's focus on game's periods of excitement (4)
I believe the answer is:
ruts
'periods of excitement' is the definition.
(periods of sexual activity for animals)
'scotsman's focus on game's' is the wordplay.
'focus' says to take the centre (focus can mean the centre of something).
'on' says to put letters next to each other.
'game' becomes 'rut' (I can't explain this - if you can you should give a lot more credence to this answer).
The centre of 'scotsmans' is 's'.
's' after 'rut' is 'RUTS'.
(Other definitions for ruts that I've seen before include "Ditches" , "gets ready for new partner" , "Deep furrows" , "Deep tracks in path" , "Grooves in the ground" .)