He was signed by St. Louis in 1962 and pitched for 4 seasons in the Cards' farm system, then made his major-league debut in September 1965. (The back of this card says "the young lefthander’s debut in the majors last season…", so Topps was off by 1 year.)
After struggling early-on in 1966, he spent most of May and June back in the minors before returning in late-June. Larry started his last 15 games, and ended up with a nice 11-5 record, led the league with 5 shutouts (all against the NL champion Dodgers), and finished 4th in the Rookie of the Year voting. The team’s rotation was led by Bob Gibson, then the other three (all with similar production) were Jaster, Al Jackson, and Ray Washburn. Jaster's edge was his age – 6 to 8 years younger than the other 2 guys.
Jaster looked to be a fixture in the rotation for years to come, but Steve Carlton (who made 9 starts in the last 2 months of 1966) and Dick Hughes (the 29-year-old rookie who seemingly came out of nowhere) soon passed him. Larry only started 23 of his 34 games (and was probably helped by the fact that Gibson missed 6 weeks with a broken leg) and by Labor Day (with Gibson's return) he was out of the rotation altogether.
With Jackson traded and Hughes in the bullpen, Larry was the #5 starter in 1968. That didn’t save him from the expansion draft, where he was selected by the Expos. He had a dismal 1-6 record for an obviously bad expansion team, and was traded to the Braves in the off-season for pitcher Jim Britton.
Jaster began the 1970 season with Atlanta, but by late-June was sent down to AAA, where he played for the rest of 1970 and all of 1971-74 - his only further big-league time was 5 games with the Braves in September 1972.
After his playing career he was a minor-league pitching coach for the Braves and Orioles.
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There were 490 single-player cards in the 1967 set. With Jaster's post, I have now featured all but 11 of those players on one of my blogs. The players from the 1967 set yet to be blogged are:
Sandy Alomar - 2B, Mets
Bob Barton - C, Giants
Jim Beauchamp - OF, Braves
Rob Gardner - P, Mets
Jim Gosger - OF, Athletics
Orlando Martinez - INF, Braves
Aurelio Monteagudo - P, Reds
Chico Salmon - INF, Indians
Carroll Sembera - P, Astros
Jim Stewart - INF-OF, Cubs
Chris Zachary - P, Astros