Starts to go around Debenham's to buy a handy tool (6)
I believe the answer is:
gadget
'a handy tool' is the definition.
(a useful device)
'starts to go around debenham's to buy' is the wordplay.
'starts to' says to take the initial letters.
'to buy' becomes 'get' (both can mean to purchase or obtain).
The first letters of 'go around debenhams' is 'gad'.
'gad'+'get'='GADGET'
(Other definitions for gadget that I've seen before include "Useful small device" , "Mechanical contrivance" , "Small mechanical device or tool" , "Small ingenious device" , "appliance" .)