Care of tree rather dull and old fashioned (5,3)
I believe the answer is:
first aid
'care' is the definition.
(first aid is a kind of care)
'tree rather dull and old fashioned' is the wordplay.
I cannot quite see how this works, but
'tree' could be 'fir' (fir tree is a kind of tree) and 'fir' is found in the answer.
The remaining letters 'staid' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...
'of' is the link.
Can you help me to learn more?
(Other definitions for first aid that I've seen before include "Instant help for the sick" , "Initial treatment for injured person before doctor arrives" , "'Immediate emergency care (5,3)'" , "Preliminary medical assistance before doctor arrives" , "Emergency medical treatment" .)