The phrase "a week eventually" is not standard and may be confusing in written English.
It could be used in contexts where you want to indicate that something will happen after a week, but the phrasing is awkward.
Example: "After much deliberation, we decided to wait a week eventually to see if the situation improves."
Alternatives: "in a week" or "after a week".
She began seeing Dr. Qualtere four times a week, eventually driving from Belmont to Saratoga.
Mr. Morris sent him a copy of "The Fog of War" and Mr. Rumsfeld responded within a week, eventually agreeing to sit for more than 30 hours of interviews in four sessions at Mr. Morris's home in Boston.
Three classes a week eventually turned into teacher training, which lead to a desire – a compulsion almost – to visit the country where yoga was born.
He worked in a warehouse five days a week, eventually saving the €1,500 [$1,709] he needed to buy professional cooking equipment.
He worked in a warehouse five days a week, eventually saving the €1,500 £1,3077) he needed to buy professional cooking equipment.
We will run a new installment of each series once a week, eventually getting to the point where we have a new comic every day.
The song they recorded that week eventually became a breakout hit that topped the Billboard Hot 100 chart this week and has sold more than 1.2 million digital copies.
He got a job as a junior lab assistant, attended a local polytechnic one day a week and eventually gained a degree in botany.
Next month, the RCCG is launching an online prayer group, which is expected to attract up to 500 participants, initially twice a week and eventually daily.
After the July 21 deal, the Standard & Poor's 500-stock index in the United States fell below 1,300 after about a week and eventually sank to its lowest level for the year.
When she arrived, the young men on campus didn't pay attention to her, so she stopped eating for a week and eventually passed out in a professor's office.
