هوايتي الجديدة رياضة المشي والركض بعد الشغل.

Because Arabic often leaves out the verb to be in the present tense.

So this sentence is a nominal sentence:

• هوايتي الجديدة = my new hobby
• رياضة المشي والركض بعد الشغل = walking and running after work / the exercise of walking and running after work

In natural English, we need is, but in Arabic the present-tense is is usually understood.

So the structure is basically:

• My new hobby Ø walking and running after work

If you want, you can also add هي for extra clarity:

• هوايتي الجديدة هي رياضة المشي والركض بعد الشغل

That is still natural and means the same thing.

هوايتي means my hobby.

It is built from:

• هواية = hobby
• ـي = my

So:

• هواية + ي → هوايتي

A useful thing to notice: when a word ending in ة takes a suffix, that ة is pronounced like t.

So even though the base word is هواية, in هوايتي you hear the t sound.

Also, learners sometimes confuse:

• هوايتي = my hobby
• هويتي = my identity / my ID

Those are different words.

Because it describes هواية, and هواية is a feminine noun.

In Arabic, adjectives agree with the noun they describe in:

• gender
• number
• definiteness

So:

• هواية is feminine
• therefore the adjective must also be feminine: جديدة

And because هوايتي is definite (my hobby), the adjective is also definite:

• هوايتي الجديدة = my new hobby

This agreement is very important in Arabic.

Here رياضة adds the idea of exercise / sport / physical activity.

So:

• المشي والركض = walking and running
• رياضة المشي والركض = the exercise/sport of walking and running

This makes the phrase a little more formal or descriptive.

In everyday Levantine, many speakers would also simply say:

• هوايتي الجديدة هي المشي والركض بعد الشغل

That sounds a bit more conversational.

So the version with رياضة is correct and understandable, but slightly more formal than the simplest everyday wording.

Yes, it works as an idafa-type phrase.

An idafa is a noun-to-noun construction, often translated with of in English.

Here:

• رياضة المشي والركض
• literally: the exercise/sport of walking and running

In this type of structure:

• the first noun is رياضة
• the second part is المشي والركض

That is why رياضة does not take الـ here.

So you do not say:

• الرياضة المشي in this meaning

You say:

• رياضة المشي

Because they are being used as named activities: walking and running in a general sense.

Arabic often uses the definite article with verbal nouns when talking about an activity in general:

• المشي = walking
• الركض = running

In this sentence, they are also part of the phrase رياضة المشي والركض, so the definite form sounds natural.

A rough literal reading is:

• the exercise of the walking and the running

That sounds strange in English, but it is normal in Arabic.

بعد الشغل means after work.

This is a very common Levantine expression.

• بعد = after
• الشغل = work / the job

In Levantine, الشغل is extremely common in everyday speech for work.
It is more colloquial than العمل, which sounds more formal or Standard Arabic.

So:

• بعد الشغل = after work
• بعد العمل = also possible, but more formal
• بعد الدوام = also common, often meaning after the work shift / after office hours

It is understandable, but it sounds a little mixed:

• الشغل is very colloquial Levantine
• رياضة المشي والركض sounds a bit more formal/bookish

So the sentence is fine, but not the most casual everyday phrasing.

A more natural conversational Levantine version might be:

• هوايتي الجديدة هي المشي والركض بعد الشغل
• صار المشي والركض بعد الشغل هوايتي الجديدة

These sound more like spontaneous speech.

Usually الركض means running, but in many everyday contexts it can cover what English speakers might call jogging too.

Arabic does not always make the same sharp distinction that English does between:

• running
• jogging

So depending on context, الركض can be understood fairly broadly.

If someone wants to be very specific, they might choose a different wording, but الركض is a normal and clear choice here.

Yes.

You can say:

• هوايتي الجديدة هي رياضة المشي والركض بعد الشغل

This is slightly more explicit and can sound smoother to some learners because it feels closer to English My new hobby is...

In casual speech, many people would more naturally say:

• هوايتي الجديدة هي المشي والركض بعد الشغل

So adding هي is absolutely possible.

Yes, Arabic word order is flexible, but changing it changes the emphasis.

The original sentence starts with:

• هوايتي الجديدة = the topic

That gives a neutral meaning: My new hobby is...

If you move the activity to the front, you emphasize it more:

• رياضة المشي والركض بعد الشغل هوايتي الجديدة

That is possible, but it sounds more marked, as if you are highlighting walking and running after work.

For most learners, the original order is the safest and most natural way to say it.