Greens periodically supported by two brilliant people (5)
I believe the answer is:
genii
'brilliant people' is the definition.
'genii' can be an answer for 'people' (genius is a kind of person). I'm not sure about the 'brilliant' bit.
'greens periodically supported by two' is the wordplay.
'periodically' means one should take alternating letters (letters must be selected 'every so often').
'supported by' means one lot of letters go next to another (in a down clue, some letters hold up others).
'two' becomes 'II' (Roman numerals).
The alternating letters of 'greens' are 'gen'.
'gen'+'ii'='GENII'
Can you help me to learn more?
(Other definitions for genii that I've seen before include "Personal spirits" , "bottled spirits" , "Spirits such as Aladdin's" , "Guardian spirits of a place" , "Demons with magical powers" .)