From the botanist's angle, side shoots may appear (4)
I believe the answer is:
axil
'from the botanist's' is the definition.
I can't tell whether this definition defines the answer.
'angle side shoots may appear' is the wordplay.
I cannot really understand how this works, but
'angle' could be 'l' and 'l' is found within the answer.
'side' could be 'xi' (a football team, from Roman numerals for 11) and 'xi' is found in the answer.
A single letter 'a' remains which might be clued in a way I don't see.
This explanation may well be incorrect...
Can you help me to learn more?
(Another definition for axil that I've seen is " Angle between leaf and stem".)