Projection from First Lady inspiring American society (5)
I believe the answer is:
eaves
'projection' is the definition.
(I know that eaves is a type of overhang)
'first lady inspiring american society' is the wordplay.
'first' means one lot of letters go next to another.
'lady' becomes 'eve' (I've seen this before).
'inspiring' means one lot of letters goes inside another.
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'society' becomes 's' (common abbreviation in names of organisations).
'eve' placed around 'a' is 'eave'.
'eave' next to 's' is 'EAVES'.
'from' is the link.
(Other definitions for eaves that I've seen before include "Overhanging part of roof" , "Roof projection" , "Overhanging edge of roof" , "Anything projecting" , "Projecting edge of a roof" .)