Most of the main characters in Game of Thrones season 4 will have a lot on their plate, and so will Davos Seaworth (Liam Cunningham), who may have his own life in danger.
Presuming the writers of Game of Thrones continue adapting A Storm of Swords, the third book in the A Song of Ice and Fire novels by George R. R. Martin, Davos won't have a lot to do, but he'll still contribute to the main plot.
In the latter half of A Storm of Swords, Davos gives Stannis (Stephen Dillane) the letter from the Night's Watch, as seen in the season 3 finale. Davos convinces Stannis to lead his army to the Wall in the hope of defeating Mance Rayder (Ciaran Hinds) and the wildlings. Stannis and his army properly defeat the wildlings, which ends up proving to Stannis that Davos is worthy to be the Hand of the King.
With Stannis taking control at the Wall, he sends Davos to the northern territories in order to spread his influence. He sends Davos to White Harbor to see the lord Wyman Manderly. However, Davos' reception is not kind as Manderly orders the beheading of Davos. By doing so, Manderly hopes to send a message about what happens when people support Stannis.
Soon, rumors begin to spread that Davos has been executed. This is where Davos' storyline ends in A Storm of Swords, though the show may throw in more scenes for him. Davos' possible beheading might be one of the show's many cliffhangers in the season 4 finale.
Game of Thrones season 4 is scheduled to premiere in spring 2014, though HBO has not yet set a specific premiere date.