Hester turned down a £963,000 annual bonus earlier this year after pressure from politicians and commentators.
But he was awarded a long-term bonus that could result in him being given up to 10.1m shares in the bank. Pensions & Investment Research Consultants (Pirc), the corporate-governance adviser, has recommended shareholders vote against the directors' remuneration report.
Pirc also opposes RBS's plan to consolidate its shares, turning 10 current shares into one new one.
The bank says this will reduce volatility and make it easier for the government to begin selling off its 82% stake. Pirc claims the move is just part of RBS's "dysfunctional" accounting standards, which hide the true nature of its losses.