As a WHM second... learn when NOT to heal. Spaming medica/medica II/cure/cure II/cure III will just deplete your MP. Not everyone needs to be topped up 100% all the time.

Learn to love the synergy with a SCH in 8 mans.

Learn both uses for Shourd of Saints in case you need either and don't be afraid to use it early if need be.

Stoneskin and more stoneskin and even more stoneskin - if you are aware of the fight and know that a tank is about to get hit by something big... cast it on the tank and they will take a lot less damage(this can be so helpful at managing something like mountain buster and whicked wheel).

The less you heal the more MP you will get back - thus not relying on MP batteries(aka bards(my main)), MP pots and Shourd of Saints.

If you need MP(and you are the one that knows if they need it or not - some are happy with 1k mp some want 50% of their pool etc...) have a macro preferably with a sound alarm next to it <se.1-15> that tells the party your MP percentage and requesting mage's ballad(and remember auto translate works in macros) if nothing else this can signal the tank that they need to pop some heavy CDs or even go Holmgang or the PLD skill to just grind through that. Use MP pots if you need to. Pop shroud if you get raised and pop a pot(I tend to rely on hi-elxisirs as both whm and brd) as well to get back into the healing game fast. If you can, drop a divine seal medica II and regen on tank at the same time so you have a breather for your MP to regen.

Divine seal - it's a great CD - learn when it's best to use it(my own choice tends to be medica II after big aoes that I know more damage is coming to the tank along with a divine seal regen on tank). Also divine seal+medica is basically a long range cure III.

Cure III know when to use it - it's rare usually. Cure and freecure should be your main unless you're doing something like speedruns.