It depends on the gear. If it's a stereo input on the outboard unit, then you will need TRS-XLR. If it's a mono input (or perhaps 2 mono inputs) then you only need TS-XLR.

-restashured

HMNP - a few tips:

For maximum flexibility, I would recommend your patchbay has TRS jacks front and rear, not mono (TS) jacks. Check that all your outboard gear has balanced ins and outs, and also delve in the operating manuals for each piece of gear and make a table of I/O signal levels. Most will be +4dBu nominal, but you need to find out the full-scale range of each, especially if some of the gear is digital inside with AD and DA conversion on the outside. The full-scale values (0dBFS) will likely be in the range +16dBu to +24dBu. Mark the values on the labels on the patchbay and take them into account when level setting after re-patching. It's all too easy to overdrive the inputs of outboard gear through making assumptions about full-scale levels.

Measure your cable runs, then buy a stack of short 1/4" TRS - TRS cables for patching and long XLR - 1/4" TRS cables for wiring to the rack gear. You will need TRS - XLR(M) for gear inputs and TRS - XLR(F) for gear outputs.

I'm assuming you are dealing with separately patched signals for right and left channels on stereo gear.

If some of your gear has unbalanced I/O, it will probably work OK, but your input levels will be 6dB lower than you expect because only one half of the balanced out will be driving it. You need to look inthe manuals again for that gear to check that XLR pin 3 is not connected on inputs and is grounded on outputs. Most gear that takes balanced inputs will give the full signal level when driven unbalanced, but the noise rejection will be not as good. If your gear has mono jack I/O, you will need to take care when wiring up the patchbay - same rules as for XLR: -ve outputs from patchbay not connected and -ve inputs to patchbay grounded.

Good luck!