Can tripwire be remotely accessed?
I mean, if I install tripwire in server, can it be checked for clients without installing tripwire in it.
I'm not exactly clear on what you are asking. Are you asking if you can check remote machines from the server without installing tripwire on the clients?
If that's your question, the answer is "maybe". If you can access the client filesystem (via SMB or NFS), you can run tripwire on the server. Note that using either of these protocols can expose your server to vulnerabilities.
If there's no such access, and everything is remote, then the answer is no. You need a tripwire binary in order to verify the files. Most people accomplish this via scp'ing over a copy of tripwire and the databases, and running it that way.
I hope that answers your question.