property left by deceased

In florida, the probate court has the authority to decline to appoint a nominated executor, and the authority to appoint an executor who was not nominated by the decedent.

Your question is not clear. You should review your facts and options with an attorney.

If you are asking whether the court (presumably in WA) can revoke the authority of the present executor and appoint another executor, the answer is "yes". See Chapter 11.28 RCW (Letters testamentary and of administration). Statutes are at: http://apps.leg.wa.gov/RCW/default.aspx?cite=11.28 .

RCW 11.28.160 (Cancellation of letters of administration) provides: "The court appointing any personal representative shall have authority for any cause deemed sufficient, to cancel and annul such letters and appoint other personal representatives in the place of those removed."

Whether the court will remove the present executor depends on the specific facts.

Unless you are willing to spend considerable time in learning the procedures and law, it may be cost effective to hire an attorney to help.

As indicated above, your question is ambiguous.
Are you petitioning to open a probate & don't want the Court to appoint the executor named in Decedent's Will?
Or has the executor already been appointed, and you want to remove the executor and have the Court appoint a replacement?

In either case, the simplest way to effect your result is to have the named executor who has not been appointed decline to serve, or to have the appointed executor who is serving resign.

If the executor wants to serve or continue to serve, you have a tough row to hoe. See RCW 11.68.070 & 11.28.250 regarding removing a PR who is serving. In general, if the PR is alive, taking action, and not abusing his or her trust, there is no cause for removal.

For further details, see: http://www.probate-litigation.com/I-Disqualification-Removal-Personal-Representative.htm