Hello, I was just wondering what the laws are with walking a dog outside of an a eruv. Can I still hold the leash or can I make it part of my belt (clipped on) is it considered carrying? My second question is can pick up after your dog when there is no eruv. I live in a big city and I would be worried about a hillul hashem if I didn’t.
Yes, one may walk a dog on Shabbat even in an area without an eruv.
Holding a leash is permitted because this is not considered standard carrying. You are not transporting the leash as an object; rather, you are holding onto the animal itself, which is moving on its own. The leash functions as a means of control, not as an item being carried. For this reason, there is no need to clip it to a belt or treat it as clothing.
Regarding picking up after the dog: leaving waste in a public place would indeed be disrespectful and can easily lead to chilul Hashem, especially in a city setting. The concern, as you noted, is carrying the bag without an eruv.
A simple and acceptable solution is to tie the bag to the leash. Many leashes already have loops or rings for this purpose, or you can add one. Keep bags attached in advance. When needed, place the waste in the bag and tie it back onto the leash. Since it is not being carried in the normal way, this is considered indirect handling (kilachar yad) and is permitted.
This is the simplest, respectful, and halachically sound approach.