The Textile Museum has appointed Patricia Fiske as director, succeeding Andrew Oliver, who resigned to pursue his interests in classical archeology. Fiske, 45, has been acting director since January.

She has been on the staff of the Textile Museum, most recently as associate curator for Old World carpets and textiles, since October 1973. Her primary scholarly interests are in post-classical Islamic rugs and Far Eastern textiles.

To date, she is best known for the museum's Moroccan exhibition and catalogue. Fiske graduated from Wellesley College, and has worked at Johns Hopkins University and the Baltimore Museum of Art. She is married to Richard Fiske, the director of the Smithsonian's National Museum of Natural History. They believe they may be the only married couple who both head a major museum.

The Textile Museum, at 2320 S St. NW, was recently remodeled to improve its exhibition and storage space. It is one of only two textile art museums in the world. Its 2,800 members and the museum staff carry on extensive scholarly, restoration and exhibition programs.

"Under Andrew Oliver, the museum attained a great degree of professionalism," Fiske said yesterday. "Now we need to go on to finish the job by remodeling the conservation facilities and the storage space for Islamic textiles. We don't need to build any more space, just redesign what we have." The museum is located in the former Myers mansion and its neighboring house, and the conservation laboratories are in the mansion garages on Decatur Place.