Prime for second time?

Hi guys.
I brewed a coopers draft, It spent 2 weeks in primary. Then 1 week in barrel at room temp then 2 weeks so far in fridge to cold condition.

i tested the brew and there was some carbonation not high but enough , As im using roto keg.

Now after two weeks in fridge i did a test to see how the brew is coming along. It is clearing up nice but is totally flat.
I used a small co2 bulb to put some gas in there only to find that its leaking on the s30 valve seal.
I do have another keg that i can transfer to that does not leak as Ive used it before.

My question is. if i transfer this brew to a new barrel it will need more priming sugar. But as it has been cold conditioning will i need to add a little extra yeast after i get it back up to room temp.

I don't think you will need to add extra yeast. IMO, it didn't spend enough time at room temp prior to cold crashing. I would move it back to a warmer area. I believe most of your yeast has fallen out due to the cold temps. Hence the reason it is clearing up, but is still flat.