An electric field could.
In theory the gravitational and electric fields could accelerate a moving electron but practically speaking for most cases only an electric field will accelerate the electron noticeably. The magnitudes of the electric and gravitational forces are a product of the charge and mass respectively with some other values.
The charge on an electron is #-1.6 . 10^-19 C# and the (rest) mass of an electron is #9.1 . 10^-31 kg#. As you can see the charge is several orders of magnitude larger than the mass. That fact combined with the constants of each equation mean that for most cases only an electric field will exert a large enough force on an electron to cause it to speed up (or slow down).
Electric force - Coulomb's Law:
Gravitational force - Newton's Law of Gravitation:
The magnetic force will not change the speed of a moving electron because the magnetic force is always perpendicular to the velocity. A moving electron in a uniform magnetic field will undergo uniform circular motion.