I wanted to apply PhD in Clinical Psychology, but my research activities and research interests are a bit different
I don't know anything about your own educational system and I can't speak for "the West" in general, but in the US you shouldn't have any particular difficulty, other things being equal. In fact, having some research experience in the general psychology area would likely be treated as a plus no matter what the focus. 

In the US, it is possible, in general to be accepted into doctoral programs with only an undergraduate education and very little if any research experience. You also don't, in general, need to specify a specialty on entry, but choose one during the first years. Such programs normally have some course work to fill in gaps. 

The path, for the US, actually, is to apply to programs that interest  you, or, at least, contact departments at such institutions and discuss your qualifications and interests. 

The European system is different, and I'll let other speak about it. But I will guess that the research process isn't vastly different between the experience you have and the degree you seek. That is an important asset. That process can be widely applied and tailored to specific areas.