be here to stay

被普遍接受，永久存在 | be permanent or widely accepted

But coal is here to stay, because it is abundant and the alternatives are generally more expensive.
Time will tell whether female-friendly foods are a passing fancy or a market niche that's here to stay.

bite the hand that feeds one

忘恩负义，恩将仇报 | to turn against someone who has been a benefactor in the past; to reflect ingratitude towards a someone who has been helpful | 後足で砂をかける

To expect that a person with such integrity will not bite the hand that feeds him is laughable. Hasn't he given you enough instances in the past about his integrity?
The fact that she bit the hand that fed her doesn't upset you even a little?

get out of bed on the wrong side

自打起床心情就不好，起床姿势不对 | to be in a bad or grumpy mood throughout the day | 虫の居所が悪い

Geez, the boss has been in a really bad mood all day. I guess he must have gotten out of bed on the wrong side!
Oh dear. Did you get out of bed on the wrong side today? You seem very angry.

have an axe/ax to grind

有私心，有个人打算 | have a private or selfish reason for doing something | 腹に一物ある

Certainly, she has an axe to grind, and a battered reputation to rebuild, and so like most political memoirs this one is one-sided.
What started as a casual discussion flared up into a heated debate because both of them had an axe to grind.

have ants in the/one's pants

坐立不安 | be extremely restless, uneasy, impatient, or anxious | 居ても立っても居られない

She was very excited to be going to the party that night and had ants in her pants all day.
Maybe it's just God trying to tell me to keep still and stop acting like I have ants in my pants, to just be calm and happy that all is well.

keep someone/something at bay

不让···接近，防止···恶化 | prevent (someone or something) from approaching or having an effect | ～を寄せ付けない。～を食い止める。

Half-a-dozen campfires were lit for the purpose of beating the chill and to keep wild animals at bay, while the forest personnel stood guard.
Prison chiefs have tightened security after an inmate climbed onto a roof and kept guards at bay for five-and-a-half hours.

long arm of the law

法网恢恢，疏而不漏 | the broad, far-reaching power or influence of the police or legal system

He added that he had all but forgotten the murder, but the long arm of the law had an even longer memory.
Be careful of committing fraud my friend! The long arm of the law will catch up with you some day or the other.

sign on the dotted line

签署具有法律效力的文件，正式同意 | to officially agree to buy or do something by signing a document

The organisers of this year's Wiltshire Festival have signed on the dotted line to allow the huge event to take place.
It's not just moms and dads fighting the middle-aged spread who are rushing to sign on the dotted line of membership forms.

the writing/handwriting (is) on the wall

不祥之兆 | the very apparent signs that something bad will happen in the future | 〔特に失敗・災害の〕兆し

This tells us that governments can read the writing on the wall and do what they can to direct and steer the legislative momentum.
Since tobacco companies market their product to young people, the handwriting is on the wall in terms of the toll that we can expect if the course continues unchecked.

up in the air

悬而未决 | uncertain or unresolved, often because other matters have to be decided first

Our vacation plans are still up in the air as we keep differing over our choice of locations.
Its own future is in doubt at this point and sources suggest the situation is now totally up in the air.