The National Football League Players Association, hoping to bolster an effort to restore players' confidence in their union, yesterday elected New York Giants veteran George Martin its new president. The union's player representatives, on the second day of a three-day meeting in Washington, elected the Philadelphia Eagles' John Spagnola as first vice-president, one of four new members to the union's executive board.

Martin, a defensive end who has been one of the key components of the Giants' defense for the last 13 seasons, will succeed Marvin Powell, who served the last two years before retiring from the position on Wednesday. Powell decided after several knee surgeries to retire as a player. An active player must hold the post of president in the NFLPA. Powell will remain a union officer, as ex-officio president.

Quite a few union officials wanted Martin to be the president two years ago, but he declined. Martin, a team representative since 1981 and a member of the executive committee since 1984, didn't come to these meetings seeking the presidency this time, either. Before last night's NFLPA awards banquet at the Washington Sheraton, Martin said he was "a little apprehensive," but decided to accept the job because, "they had faith in me . . . I was so honored."

Martin said his "first mandate is to do less talking and more listening . . . listening to the board of representatives and players."

After Martin was elected overwhelmingly (no vote count was given), Powell handed the new president a box of Tylenol, the union's executive director, Gene Upshaw said. "He told George, 'You'll need these.' "

Martin, Mick Luckhurst and Mike Kenn of the Atlanta Falcons, Mike Davis of the San Diego Chargers (second vice-president) and Miami's Dan Marino were all reelected to the executive committee; the Raiders' Sean Jones, Denver's Ricky Hunley, San Diego's Wes Chandler and Spagnola are the new members.

Together, they hope to restore some of the confidence players may have lost in the union following the 24-day players' strike that ended without a new collective bargaining agreement after the 28 NFL owners put on games with replacement players.

Luckhurst said the union officials feel that "renewing the confidence of the players in the union," is the first step in a healing process . . . I had a lot of questions when I first came to these meetings, but I feel very good about the future of the union right now."