Making the Rounds solution
by Kegler

Five answers start with REP, but each REP “travels” to another answer before entry, as hinted at by 26A's unclued TRAVELING SALESMEN.

Making the Rounds solution grid

Across
1E(PIG)RAPHS (PHRASE anag)
7{REP}ROACH (hidden)
12GA(E)L
13METEOR (REMOTE anag)
14K + I'D
16LEILA (hidden)
17G + R + ASPS
19CU(T)E
20TOLD (DOLT anag)
22AVARIC + E (CAVIAR anag)
24P + O(LICE)MEN
25PALER + MO
26TRAVELING SALESMEN
29IN + VA + LID
30{REP}E(A + TIN)G
32{REP}AINT (TINA anag)
34B(R)AT
35ABUT (hidden)
36G + RATIS (SITAR rev)
37{REP}LAC(E)S (SCALPER rev)
38LOX (2 defs)
39E(ME)NDS
40MOTH (1st letters, &lit)
41{REP}R[I/o]SES
42EDELWEISS (SWEDES LIE anag)
Down
1ELLIPTICAL (I'LL PLACE IT anag)
2PREdaTOR
3GALLIVANTER (A TRAVELLING anag)
4RE(A)D
5P(A + R)A
6HEAVE(NWARD)S (DRAWN rev)
7{REP}RE(SENT)ED
8P + E + RCALES (CLEARS anag)
9{RE(P}RO)VE
10pORCH + EST(R)ATE
11CITE ("SIGHT" hom)
15DECONGESTS ("DEACON JESTS" hom)
18SANG + aRIA
21RELI(E)VES
23A + R + M
27{R(E + P)}AVE
28{RE(P},E)NTERS
31hOBOEs
32RAM + I
33{RE(P)}TILE
34B(L)OW