I think I can help with that, the answer to 'allowed to strike' in the NYT crossword is likely 'oncall', it's a common phrase that fits the description, as it refers to being available to work or take action when needed, which can include striking, but another possible answer could be 'unionized', as being part of a union often means being allowed to go on strike, see if either of those fit the available letters in your crossword.