Plant not that tilted, oddly (7)
I believe the answer is:
thistle
'plant' is the definition.
(type of plant)
'not that tilted oddly' is the wordplay.
'not that' becomes 'this' (this one as opposed to that one).
'oddly' indicates alternate letters (letters in the odd-numbered positions are used).
The alternate letters of 'tilted' are 'tle'.
'this'+'tle'='THISTLE'
(Other definitions for thistle that I've seen before include "Prickly plant with purple flowers" , "Flower of Scotland" , "Scots plant emblem" , "...Partick" , "Prickly plant, emblem of Scotland" .)