Use Stoneskin liberally while in Cleric Stance. Stoneskin always shields for a set amount (18% of max HP) even in cleric stance.

Use <tt> macros to reduce the amount of target switching you need to do. <tt> = target of target. Here's an example:

/micon "Stone II"
/ac "Stone II" <t>
/ac "Stone II" <tt>

The first line enables the Stone II icon for your macro. The second line casts Stone II on your target if it's an enemy. The third line casts Stone II on the target of your current target (you cast on whatever your tank is attacking). This lets you deal damage and heal without ever having to switch targets manually in a party. If you're solo, it functions as usual.

Learn what tank cooldowns do and memorize what the buff icons look like. This lets you know when the tank won't need heavy amounts of healing. This is especially useful in WP speed runs.

Know the abilities of the enemies you're fighting so that you can predict spike damage. For example, the Tonberry King's ability Everyone Grudge deals ~1,000 dmg per stack regardless of abilities like shield oath and rampart. If that boss has 4-5 stacks, get out of Cleric Stance and make sure your tank is topped off and has Stoneskin. If you understand all the possible sources of incoming damage, it's easy to know when you're free to deal damage safely.