If using actual PAINT...YES...Definitely.
Maybe even 2 coats of primer...IF it's very thirsty, and a cheaper primer is used.

IF using solid STAIN...No...priming is totally optional.

Faron

I think Faron missed that this is rough sewn cedar, so skipping primer is really not going to work because of the tannin bleed. If I were doing the repairs, I would cut all the cedar, then prime all sides, especially the end cuts and then install it. I know this isn't always feasible, but IMO it's a pretty silly idea to install raw cedar anywhere outside if you have the option of priming it before installation. Backpriming helps to block out moisture on all sides which will give the wood a longer life. You also need to use an oil based primer, preferably a slow drying one. The fast drying oil based primers are okay, but you get a better bond with a slow drying process. Latex primers will not work because there are stains in the cedar like tannin that will bleed right through them.

PG....yeah, I knew it was rough-stuff. That's why I stated the possibility of even TWO coats of primer, if using Paint.

Priming under Stain...well...if a "Fairly Rustic" look is desired, stain away!
BUT...AS PG SAYS...PRIME ALL THE WAY AROUND if you have a choice, for exactly the reasons he says.

It's just stupid NOT to!!

Faron

I had two painters come out and they said it was painted before, so it must be painted again.