First of all, it is entirely unclear what the Presidential science advisor actually does.

In general, the position is inhabited by unremarkable or not very distinguished scientists and they have varying terms of service but they can span administrations.

Historical List:

FDR:

• Vennevar Bush 1941-1945

Truman:

• Vennevar Bush 1945-1951
• Oliver Buckley 1951-1952
• Lee Alvin Dubridge 1952-1953

Eisenhower

• Dubridge 1953-1956
• Isidor Isaac Rabi 1956 - 1957
• James Killian 1957-1959
• George Kistiakowsky 1959-1961

Kennedy:

• Jerome Wiesner 1961-1963

LBJ

• Jerome Wiesner 1963-1964
• Donald Hornig 1964-1969

Nixon

• Lee DuBridge 1969-1970
• Edward David 1970-1973

Ford:

• H. Gurford Stever 1976-1977 (note 3 year gap)

Carter

• Frank Press 1977-1981

Reagan:

• George Keyworth 1981-1985
• William Graham 1986-1989

Bush:

• Allan Bromley 1989-1993

Clinton

• John Gibbons 1993-1998
• Neal Lane 1998-2001

Bush Jr:

• John Marbuger 2001-2009

Obama

• John Holdren 2009-2017

Now, two year gap until Trump appoints this guy


Choosing a Presidential Science Advisor

A candid view from a former Presidential Science Advisor To quote:

Finally, any suspicion that the science advisor has come to the White House with the primary objective of increasing funding for research, rather than supporting the president with confidential objective advice, severely limits the science advisor's credibility and effectiveness. Nixon's advisor, DuBridge, was excluded from budget discussions after arguing for increases in NSF's budget. Although it is understood that the science advisor is likely to be an advocate for S&T, including R&D funding, any arguments for increased funding must be linked to the president's top priorities. To put it in the simplest terms, the science advisor must be relevant, objective, and loyal to the president and stay out of trouble; even trouble that is not of his own making.