How to do research after Ph.D when you have less time?
There are a few ideas. The first is to set aside some time each week for your own research. A few hours in a block, perhaps. 

The next is to keep a research notebook (or a small pack of index cards) with you at all times so that you can (a) review existing cards and (b) jot down any ideas that occur. Especially keep ideas for things that might be explored when you have he time. 

Third, and very important, is to develop a circle of collaborators wherever you can find them. If not possible at your own university, perhaps at a nearby one. But there are also conferences that you can probably attend and meet people with similar interests. Follow up with authors of papers you find interesting. Modern communication makes even international collaboration quite easy if you all write a common language. 

Doctoral study is very intense and most people have few obligations other than the research. That changes for many upon graduation, especially if teaching is a big part of the job. But you can also interest a few advanced undergraduates in your research, perhaps.