Texas Pacific Land Trust, a once-moribund land bank that became one of the hottest shale stocks, needs to modernize its Wild West-era corporate governance structures after boosting the pay of its top two executives 10-fold since 2016, one of its biggest investors said.

Chief Executive Officer Tyler Glover, and Chief Financial Officer Robert Packer, each received $2.3 million in salary and bonuses in 2018, up from $201,000 and $225,000 respectively in 2016, when they began the roles, according to a...