If you increase your player level, does the max cp of your pokémon increase?

Your player level impacts the maximum CP level of all Pokemon, not just the ones you catch after levelling.

You can clearly see this mechanic by comparing the CP circle behind the Pokemon. After you level up, the "filled in" area will decrease, to reflect the increased maximum.

You may notice higher CP Pokemon also spawn, as your higher trainer level also allows you to catch higher CP Pokemon.

CP of all Pokemon scale with your character.

Every Pokemon has a (so far) unknown value that is considered their true "Max CP." At each Trainer Level, the game decides the Pokemon's current CP cap based on your level with a (so far) unknown formula.

However, the multipliers that are used to calculate how strong a Pokemon is are as follows:

L1: 0.094
L2: 0.16639787
L3: 0.21573247
L4: 0.25572005
L5: 0.29024988
L6: 0.3210876
L7: 0.34921268
L8: 0.37523559
L9: 0.39956728
L10: 0.4225
L11: 0.44310755
L12: 0.46279839
L13: 0.48168495
L14: 0.49985844
L15: 0.51739395
L16: 0.53435433
L17: 0.55079269
L18: 0.56675452
L19: 0.58227891
L20: 0.5974
L21: 0.61215729
L22: 0.62656713
L23: 0.64065295
L24: 0.65443563
L25: 0.667934
L26: 0.68116492
L27: 0.69414365
L28: 0.70688421
L29: 0.71939909
L30: 0.7317
L31: 0.73776948
L32: 0.74378943
L33: 0.74976104
L34: 0.75568551
L35: 0.76156384
L36: 0.76739717
L37: 0.7731865
L38: 0.77893275
L39: 0.784637
L40: 0.7903

The current theory (at the time of my editing this post) is that this is multiplied by a Pokemon's "Max CP" to get the value that decides their current CP cap. If this holds true, this table gives you an example of exactly how much CP levels scale up.

Pokemon in the wild will also be relatively stronger than they used to be. However, wild Pokemon will not increase in strength after you hit Level 30.

^{Data sourced from a data dump of mine}