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56a Shot provider of duff gen on country at war briefly
I have E-r----
50aSatellite receiver to come down after swapping three components
-U-I----
54a What garden's left with after hurricane's finished off?
N-s-e-
46d Old judge of mine, reflecting over a long period.
---e--
47d Beef joint presented by wife.
---n--
Thanks in advance for any help.

Hi sazdaw, you have a couple of errors.
56a. Syri (a) + nge (anagram of gen)
50a. Minidish => diminish
54a. No shed
46d. Gideon, dig reversed + eon
47d. W + hinge

Whew, thanks ginge. I had thumb muscle for 37 down -
They can be depressed by what it takes to hitch hike!
No wonder I was stuck.
I guess it must be thumb pieces?

37d is Thumbsticks, got it at last!:

Not Thumbsticks of course, it doesn't fit!! Must be thumb pieces but that's two words!

I think thumbpieces is one word (or possibly hyphenated, which often means one word in crosswords!) in Chambers. I can't check just now.