The dispute concerns maritime pilots who navigate ships - including cruise ships - in and out of the UK’s waterways and ports.
Vessels cannot leave or enter UK’s ports without these workers, who have expert knowledge of the weather, tides, water depths and traffic management.
Unite said ABP introduced increased medical standards at ports without any consultation last July.
The trade union added that a consultation is required under health and safety legislation and its recognition agreement with ABP.
An ABP spokesperson said: “ABP is continuing to engage with our recognised trade unions and we are hopeful of reaching a resolution.