Teacher's perhaps after hard work and playground activity (9)
I believe the answer is:
hopscotch
'playground activity' is the definition.
(playground game)
'teacher's perhaps after hard work' is the wordplay.
'teacher's perhaps' becomes 'scotch' (Teacher's Scotch, brand of whisky).
'after' says to put letters next to each other.
'hard' becomes 'h' (abbreviation used in pencil classifications).
'work' becomes 'op' (common abbreviation for 'opus').
'h'+'op'='hop'
'scotch' after 'hop' is 'HOPSCOTCH'.
'and' is the link.
(Other definitions for hopscotch that I've seen before include "kids jump about in it" , "Jumping game" , "Playground game" , "Children's pavement game" , "Traditional children's game" .)