For the act of consuming something:
* Ingest
* Consume
* Gobble (implies eating quickly)
* Gulp (implies swallowing quickly)
* Swig (implies swallowing a large amount of liquid)
* Down (informal, often used for drinks)
* Take (can be used for both food and drink)
* Devour (implies eating greedily)
For the act of suppressing feelings:
* Suppress
* Conceal
* Hide
* Bottle up
* Hold back
* Endure
For the act of accepting something:
* Accept
* Tolerate
* Endure
* Bear
* Put up with
* Submit to
The best synonym will depend on the specific context of your sentence.