Was it ever determined who paid for the defence team in the trial? I believe I read at some point that KR is a private attorney but of course that doesn't mean that he didn't take on the case at legal aid rates.
If he was actually hired by DG's family, and they are willing to pay again, they may hire an appellate attorney for DG. Some attorneys do both, but some just specialize in appeals.
If DG applied for and received legal aid to pay his defence team, then I believe he would have to do the same for an appellate attorney. I know that in Ontario, legal aid does not have to provide appeal funding if they don't think there is a chance. However both Michael Rafferty and Paul Bernardo fought for funding under section 684 of the criminal code and won. Both of their appeals were rejected anyway. Just a waste of taxpayer money. Not sure if it's the same in Alberta.
It's entirely possible that KR will help DG to file an appeal. It sounds like he is staying in contact with him so I can see him doing that at the very least. They have 30 days from the conviction.
MOO
http://laws-lois.justice.gc.ca/eng/regulations/SI-2012-39/page-1.html
http://www.lfpress.com/2013/05/17/rafferty-hoping-taxpayers-bankroll-lawyer-for-appeal