Gunslingers spend grit points to accomplish deeds. Most deeds grant the gunslinger some momentary bonus or effect, but there are some that provide longer-lasting effects. Some deeds stay in effect as long as the gunslinger has at least 1 grit point. The following is the list of base gunslinger deeds. A gunslinger can only perform deeds of her level or lower. Unless otherwise noted, a deed can be performed multiple successive times, as long as the appropriate amount of grit is spent to perform the deed.
From the RAW (Rules As Written) it seems that using deeds is not classified as an action unless noted by the specific deed (think of how melee characters use the power attack feat for example; either applying it to attacks for that turn or not). Therefore as long as you have the grit to spend you should be all good to use multiple deeds in a single turn if applicable.
In your case, both deeds would work together in a single round. One of them is a full round action while the other is not an action. As long as you have enough grit you could use them together in a single round.
Also as a side note you could do something like use the quick clear deed in one round twice.
Let's say you were two weapon fighting with a pistol in each hand and last turn you misfired both of them. This turn you could spend your standard action to quick clear the first pistol then spend your move action and 1 grit to quick clear the second pistol.
One last thing to note. An example of not being able to use 2 deeds in one turn would be dead shot and quick clear since you would need to use a standard or move action (or both as noted above) to use quick clear, preventing you from using dead shot.
