Thanks to the commenters, we’ve got the following pieces of highly exquisite gold:
1 down: Safe cushy job in shed (6)
Here, cushy job = sinecure giving cushy job in shed = secure = safe (very nice use of shed as a verb rather than a noun).
5 across: She’s hot to trot — yet inert after big apple? (6)
This clue is one part nasty to two parts gold. The brilliant piece of nastiness comes from inert = mpho, which is an inspired shorthand for zero miles per hour. With that we then get big apple = ny, giving yet inert after big apple? = nympho = she’s hot to trot.
9 across: Princess stops old Israel national siding with America (8)
Again, another inventive use of a word, in this case siding. What we’ve got here is princess = di and old Israel = canaan, which gives princess stops old Israel = canadian = national siding with America (where siding takes on the meaning of bordering in this instance).
13 across: Old redhead composer in cuckoo grove (9)
Wonderful reference to a political leader with composer = bach and cuckoo grove = gorev giving composer in cuckoo grove = gorbachev = old redhead.
7 down: Fledgling detainee singularly supported infinite truce (8)
This is perhaps one of the most difficult and brilliant clues DA has ever created. Detainee = hicks, detainee singularly = hick, truce = peace and infinite peace = peac (something infinite is endless), all of which means detainee singularly supported infinite truce = peachick = fledgling.
8 down: Sick of what you see in summary (8)
Yet again, DA invents. Sick of = over (think slang) and what you see = view, so that sick of what you see = overview = summary.