What do you do after you get Palkia to join your team in Pokemon mystery dungeon explorers of time?

After Recruiting palkia.... there are several things to do..... You can recruit Dialga and evolve after defeating Darkrai... And you can recruit the three lake Pokemon (Uxie, Mesprit, Azelf) After the first ending of the game and you restore time..

There are also the Marowak Dojo mazes... if you haven't done those yet....

In time and darkness... Suicune, Moltres, Jirachi are found in the final maze

In sky they are found in dungeons.. after you receive challenge letters from them...

There are those "Special Episodes" in sky version.... you can do those after you unlock them in the game... the last one unlocks after the whole restore time thing...

There are also those "Mystery Missions" the ones with the 7 treasures.... you can do those.... I'm sorry but the mail codes slipped my mind right now... I can tell you what they are, where they are and their guardians though as well as what they do..

Terra Cymbal- makes recruiting ground type easier- Shimmer Dessert B10F-Groudon

Grass Trumpet- makes recruiting grass types easier- Mystery Jungle 30F-Mew

Icy Flute- makes recruiting ice types easier- Mt. Avalanche 20F- Articuno

Fiery Drum- makes recruiting fire types easier- Giant Volcano 20F- Heatran

Rock Horn- makes recruiting rock types easier- World Abyss B30F- Giratina

Sky Harmonica- makes recruiting flying types easier- Sky Stairway 50F- Rayquaza

Aqua Monica- makes recruiting water types easier- Bottomless Sea B50F- Kyogre

They will eventually join your team... some right away.. others not until later... you will always get the treasure if you go back and defeat the guardian though... if the guardian joined your team... you can get the treasure without fighting it... so there is no need to worry if you lose your 7 treasures... just go back and get them again....

Or there's always the option of job offers and sentry duty (sentry duty is an easy way to get reviver seeds) :)