I have a problem with how DnD 5e handles summoning and binding extraplanar beings to your service, and I have a question for you on the issue.
If you wishe to have a creature such as a celestial, elemental, fey, or fiend bound to you for a period of time longer than one hour of concentration you need to use the spell Planar Binding to, well, bind it to your current plane and your service.
The problem arises at the intersection of the following facts:
Summoning and Conjuring spells always have a concentration duration, and the summoned creature dissapears either when concentration is broken or shortly thereafter.
"When you cast a spell with a casting time longer than a single action or reaction . . . you must mantain you concentration while you do so." (PHB, pg. 202)
"You lose concentration on a spell if you cast another spell that requires concentration. You can't concentrate on two spells at once." (PHB, pg. 203)
Planar Binding has a casting time of 1 hour (PHB, pg. 265)
Because of these facts of DnD 5e, if you summon a creature and then go to cast Planar Binding on the creature your concentration will be broken on the spell that summoned the creature and it will dissapear before you can finish casting the spell.
The only true exception to this is Conjure Elemental which is unique due to the fact that if "your concentration is broken, the elemental doesn't dissapear. Instead you lose control of the elemental . . . and it dissapears 1 hour after you summoned it" (PHB, pg. 225).
As I've layed it out currently, Planar Binding can only be used in combination with the Conjure Elemental spell. However, there is yet hope. Planar Binding does point out that typically one summons a creature into an inveted Magic Circle first, so let us look there.
Magic Circle has the following property of interest;
"The creature can't willingly enter the cylinder by nonmagical means. If the creature tries to use teleportation or interplanar travel to do so, it must first succeed on a Charisma saving throw." (PHB, pg. 256)
Thus, when inverted a creature would have to make a Charisma saving throw to leave the cylinder via interplanar travel, and our great question arises.
Is a summomed creature willingly returning to it's home plane using interplanar travel once the spell that summoned it ends, or is the summoner using interplanar travel on the summoned creature as an unwillingly target to send it back to its home plane?
Does a summoned creature return home of its own will and power once the summoning spell ends?
Yes, thus it could be trapped by Magic Circle and then bound by Planar Binding
No, thus it could not be trapped by Magic Circle nor bound by Planar Binding












