Q. For one that accepted Shabbos early, is it necessary to eat more bread after nightfall when in the case of having eaten an early Shabbos seuda?

A. Although not necessary, it is indeed proper to eat after nightfall a Kezais (olive volume) of bread, to comply according to all opinions with the mitzva of having that seuda on Shabbos.

See Mishna Berura (267: 5) that rules that on the onset, one should wait and eat Kezais of bread at night, to comply with the mitzva of Seudas Shabbos in the proper time.

The above may be helpful also to remind the early receivers of Shabbos to read the Shema at the proper time.

Horav Shlomo Moller’s Shlit’a opinion is similar.
Rabbi A. Bartfeld as revised by Horav Shlomo Miller, Horav Dovid Pam, Horav Aharon Miller and Horav Chanoch Ehrentreu Shlit’a