Here's a stab at it... I don't have too much time to optimize it but it should get you in the right direction.

I've removed all the SOQL from the loop and instead built a map relative to what logic you were doing in the code. As this was written on the fly it may not compile immediately.

public approval_dynamic_differential()
{
    Dynamiclist = new list< Dynamic_territory_differential>();
    UserTerritory ustr = [Select TerritoryId ,UserId From UserTerritory where UserId = :UserInfo.getUserId()];
    
    Map<Id, Territory> terrMap = new Map<Id, Territory>([SELECT Id ,name FROM Territory where ParentTerritoryId =:ustr.TerritoryId]); 
    //Map for user territory based off the Id of Territory Id
    //Key -> Territory Id
    //Value -> User Territory for that territory Id
    Map<Id, UserTerritory> userTerritoryMap = new Map<Id, UserTerritory>{};
    //Contains all the User Ids being processed from the user territory map
    Set<Id> userIds = new Set<Id>{};
    //Account Map for the accounts to transfer
    //Key-> Owner Id
    //Value -> Account
    Map<Id, Account[]> accountsToTransfer = new Map<Id, Account>{};
    //Account map for the accounts to update
    //Key -> OwnerId
    //Value -> Account
    Map<Id, Account[]> updatedAccounts = new Map<Id, Account>{};    
    
    for (UserTerritory user = [ SELECT Id, UserId, User.Name, TerritoryId FROM UserTerritory WHERE TerritoryId IN :terrList.keySet())
    {
        userIds.add(user.UserId);
        userTerritoryMap.put(user.TerritoryId, user);
    }
    
    for (Account a : [ select id,name,Active__c,Specialization_differential__c,Reason_For_Change__c ,Approval__c,Billingcity,Billingstate,Original_Calls_Total__c,Notes__c, OwnerId from Account WHERE OwnerId IN :userIds and Approval__c='Pending'and Submit__c=True ])
    {
        Account aList = accountsToTransfer.get(a.OwnerId);
        
        if (aList == null)
        {
            aList = new Account[]{};
            accountsToTransfer.put(a.OwnerId, aList);
        }
        
        aList.add(a);
    }
    
    for (Account a : [select id,name,Active__c,Approval__c,Specialization_differential__c,Billingcity,Billingstate, OwnerId ,(select id,name,Original_CallString__c,Updated_CallString__c,Call_String_Status__c from Call_Strings__r where Call_String_Status__c='Pending') from Account WHERE OwnerId IN :userIds and Approval__c!='Pending' and Submit__c=True])
    {
        Account aList = updatedAccounts.get(a.OwnerId);
        
        if (aList == null)
        {
            aList = new Account[]{};
            updatedAccounts.put(a.OwnerId, aList);
        }
        
        aList.add(a);
    }        
    
    for(Territory terr : terrMap.values())
    {         
        UserTerritory user = userTerritoryMap.get(terr.Id);
        User userid = terr.User;
        
        TransferAcc = accountsToTransfer.get(user.UserId);        
        UpdateAcc = updatedAccounts.get(user.UserId);
        
        d1= new Dynamic_territory_differential();
        d1.TerritoryId = terr;
        d1.userTerrid = user;
        d1.username = userid;
        d1.Accountslist = TransferAcc;
        d1.UpdateAcclist = UpdateAcc ;
        Dynamiclist.add(d1);
        system.debug('size======='+d1.UpdateAcclist.size());
        
    }
    
    getdynamicdifferential();
    
}