Federal employee filed a appeal due to initial decision from MSPB. Will I receive a brief from the opposing side if they file?
Yes. Rule 31 of the Federal Rules of Appellate Procedure (FRAP) require that briefs be served on the opposing party as well as filing them with the Court. Note that multiple copies of the briefs are required.
What else should be happening and what happens if they do not file their brief?
There is no requirement that the MSPB or the agency (depending on the nature of your appeal) file a responding brief. The statute tells the Appeals Court to review the matter on the record of the MSPB proceeding and the standard to be used in that review. Specifically, it says:
In any case filed in the United States Court of Appeals for the Federal Circuit, the court shall review the record and hold unlawful and set aside any agency action, findings, or conclusions found to be--
(1) arbitrary, capricious, an abuse of discretion, or otherwise not in accordance with law;
(2) obtained without procedures required by law, rule, or regulation having been followed; or
(3) unsupported by substantial evidence;
except that in the case of discrimination brought under any section referred to in subsection (b)(2) of this section, the employee or applicant shall have the right to have the facts subject to trial de novo by the reviewing court.
5 U.S.C.A. § 7703(c).
I should tell you that these reviews are tough to win. The Congressional Research Service (CRS), which is an office of the Congress that researches issues and produces reports to Congress on various federal issues, stated in a 2019 report about the MSPB:
Under this standard of review, the Supreme Court has recognized that the Federal Circuit’s ability to review the merits of MSPB decisions is “extremely narrow.” As the Court has further explained, in examining these MSPB decisions, “it is not for the Federal Circuit to substitute its own judgment for that of the Board.” Accordingly, the Federal Circuit typically upholds Board decisions. According to a 2019 MSPB report, over the past few years, the Federal Circuit has affirmed Board decisions in 93 to 96 percent of the cases it reviewed.
I mention this not to discourage you in your appeal but rather so you are realistic about the chances of success and don't get your hopes sky high for a win. I wish you the best of luck with it — some employees do win — just know it's not easy.