"They need permission to play."
Translation:Eles precisam de permissão para jogar.
To give a slightly more complete reply, although in English infinitives are usually quoted like so: ‘to eat’ because ‘to’ is used as a kind of dummy preposition in many cases, only ‘eat’ is the actual infinitive, a fact that is immediately obvious when you compare English with other Germanic languages.
The ‘to’ in ‘permission to play’ is a preposition that indicates a goal, you can substitute ‘in order to’. In this sense it translates as ‘para’. ‘Para + inf’ can usually be translated as ‘in order to’, ‘to’ or ‘for’.
The absence of ‘to’ doesn't mean that you don't have a preposition in Portuguese, and vice-versa.
These modal verbs get no preposition:
■ can/could may/might must shall/should will/would
■ ■ poder conseguir dever ir
In English, these get ‘to’ depending on meaning and context. In Portuguese it depends on the verb:
■ dare need (+to)
■ ■ ousar atrever-se+a necessitar+de precisar (but ‘precisar de fazer’)
Verbs that get an object + bare infinitive in English get the same in Portuguese, but I've found an exception:
■ hear see watch c. bid let make have
■ ■ ouvir ver olhar c. mandar deixar fazer (but ‘ordenar a’)
The following get ‘to’ in English, but no preposition in Portuguese:
■ desire hope ‘know how’ resolve try +to
■ ■ desejar esperar saber resolver tentar
As someone who's still learning, I find it infuriating that on-line dictionaries don't mention these things. When I was still a school boy, my Latin word-list always listed words completely with any prepositions and such. Why can't on-line dictionaries do that?