Work in the garden for Dr Arnold, say? (8)
I believe the answer is:
deadhead
I believe this is a double definition.
'work in the garden' is the first definition.
(deadheading, pruning dead flowerheads)
'dr arnold say?' is the second definition.
(famous headmaster of rugby school)
'for' is the link.
(Other definitions for deadhead that I've seen before include "Remove finished blooms" , "Remove faded blooms from" , "Treat rambler, perhaps" , "One doesn't pay to get in" , "Remove faded flowers from a plant" .)