Two figures are redrawn and merged into one. Are reproduction permissions required in this case?
Combining other people's published figures to create a new figure does not allow you to waive requests for permission to reproduce a figure. Each individual component is someone else's intellectual property, and they have the right to be credited for the work. Note that many journals have simple mechanisms for requests to reproduce, and usually it's just a matter of asking for the necessary permission.

Simply redrawing someone else's figures for a part (a) and (b)-type figure does not spare you from requesting permissions. If you have completely redrawn and combined figures (for example, to illustrate how the two figures are more closely connected than in the originals), then you are creating a new intellectual contribution. You need to cite the original work that you've adapted, but you would not be reproducing the figures, and therefore would most likely not need to secure reproduction permissions.